lesson 4 - annuity (ordinary).pptx

7/26/2019 Lesson 4 - Annuity (Ordinary).pptx

1/37

Annuities


2/37

Annuity is a series/sequence ofpayments (usually equal) made at equal

intervals of time.

Installment payments

Monthly payments/rentals

Insurance premiums

Monthly retirement benefits Weekly / monthly waes


3/37

Types of Annuity

1.Annuity Certain Annuity payable for a denite duration

Payments begin and end at xed times

2. Contingent Annuity orAnnuity Uncertain

Annuity payable for an indenite

duration (beginning or termination isdependent on some certain event)

Payments are not certain to be made


4/37

Kinds of Annuity Certain

Simple AnnuityThe interest conversion

period () is eual to the

payment interval ()

General AnnuityThe interest conversion

period () is not eual tothe payment interval ()


5/37

Classication of SimpleAnnuity

Ordinary Annuity

Annuity in "hich periodic payment () is made atthe endof each payment interval.

Annuity Due()Annuity in "hich periodic payment () is made atthe beginningof each payment interval

Deferred Annuity()Annuity in "hich periodic payment () is neither atthe beginning nor end of each payment intervalbut some later date.


6/37

!OR"U#AS

!inding ! $%en gi&en A !inding A $%engi&en !

Finding P when given A Finding A whengiven P

#ource$ #ullivan% &illiam '.% lin . &ic*s and +ames T. ,uxho-. (2/). 0'00' 34045%16T78. Pearson9Prentice 7all. p1:916

+=

i

iAF

n 1)1(

+

+=

n

n

ii

iAP

)1(

1)1(

+=

1)1( ni

iFA

+

+=

1)1(

)1(n

n

i

iiPA


7/37

!OR"U#AS

Finding F when given A Finding A whengiven F



+=

i

iAF

n 1)1(

+

+=

n

n

ii

iAP

)1(

1)1(

+=

1)1( ni

iFA

+

+=

1)1(

)1(n

n

i

iiPA

;niform

#eries3ompound

amountfactor


8/37

!OR"U#AS




+=

i

iAF

n 1)1(

+

+=

n

n

ii

iAP

)1(

1)1(

+=

1)1( ni

iFA

+

+=

1)1(

)1(n

n

i

iiPA

#in*ingfund factor


9/37

!OR"U#AS




+=

i

iAF

n 1)1(

+

+=

n

n

ii

iAP

)1(

1)1(

+=

1)1( ni

iFA

+

+=

1)1(

)1(n

n

i

iiPA

;niformseries

present

"orth factor


10/37

!OR"U#AS




+=

i

iAF

n 1)1(

+

+=

n

n

ii

iAP

)1(

1)1(

+=

1)1( ni

iFA

+

+=

1)1(

)1(n

n

i

iiPA3apital

recoveryfactor


11/37

A man deposits P 12%2every end of / months in anaccount paying


12/37

A car "as bought "ith ado"n payment of P2%and P1@% at the end ofevery month for 6 years to

discharge all principal andinterest at the rate of 12=compounded monthly. ind

the cash value of the car.


13/37

An ,8 television set ispurchased "ith a do"npayment of P6% and

P:%/2:.


14/37

rs. AlvareB pays P2


15/37

!ow much monthly deposit must be

made for " years and " months in

order to accumulate # $%&'&&& at

$" compounded monthly


16/37

What sum will be paid at the end of

each quarter for * years and * months'

if the present value is # "&'"&& andinterest is paid at $& compounded

quarterly


17/37

+ino wants to buy a car worth

#,-&'&&&. !e can pay -& of the

price as down payment and the balance

payable every end of the month for *&

months' how much must he pay

monthly at $" compounded monthly


18/37

#am wants to have # ,"&'&&& at the endof " years for her raduation epenses.

he plans to deposit a certain sum' to

achieve this at the end of each month.If her bank pays $" compounded

monthly' what should be the amount of

her monthly deposit


19/37

!ow much must be paid for -0 monthsto settle an obliation of # $%1'-&&' if

money is worth $% compounded

monthly


20/37


21/37

$. A man deposits #$%'%&&every end of * months in

an account payin " 2

compounded semi3annually. What amount is

in the account at the end of

4 years and * months

SEATWORK


22/37

%. A home video entertainment set

is offered for sale for #$0'&&&

down payment and #$0&& every 1

months for the balance' for $0

months. If interest is to be

computed at $& converted

quarterly' what is the cash priceequivalent of the set


23/37

3. On May 31, 2007, Connie invested P

185,000 at 10 !o"#o$nded "ont%&y.

T%e invest"ent is to 'e #aid o$t in (0

e)$a& "ont%&y #ay"ents *it% t%e +ist

#ay"ent on -$ne 30,2007. W%at is t%e

sie o+ ea!% "ont%&y #ay"ent/

. Co!oy *ants to a!!$"$&ate P 230,000 in

(.5 yeas. E)$a& de#osits ae "ade at t%eend o+ ea!% )$ate in an a!!o$nt t%at

#ays 15 !o"#o$nded )$ate&y. W%at

is t%e sie o+ ea!% de#osit/


24/37

indin t%e

4TEREST RATEo+ an Ann$ity


25/37

$.) olve for i usin the quadratic formula5

67ype $5 use the minus sin of the quadratic formula

67ype %5 use the plus sin of the quadratic formula

%. After solvin for ' find 5

where Type I: F and A aregiven

Type II: P and Aare given

a

b

c

where Type I: F and A aregiven

Type II: P and Aare given

a

b

c


26/37

8.A. 9orporation is plannin to

create a fund by depositin

#$'"%& every quarter for 0 years

in a bank that promises to pay afied rate over the entire term.

:ind the rate converted quarterly

if the amount in the fund at theend of the term is #*&'&&&.


27/37

;ovo


28/37

At $%at nominal ratecompounded (uarterly ist%e loan of )*+,--- .e paid

$it% e(ual payment of)/,*-- at t%e end of eac% 0mont%s for 1 years2


29/37

If # "'&"& periodic payment per

quarter for $& 2 years amount to #

""&'&&&= what is the rate of

interest


30/37

$.) If # "'&"& periodic payment per quarter for $& 2

years amount to # ""&'&&&= what is the rate ofinterest

%.) :ind the interest rate compounded semi3annually

on #--'-&& whose periodic deposit of # -'-&&every end of si months for * years and * months.

1.) A dinin set worth # $%'%&& cash is purchased by

a down payment of # "'0&& and monthly paymentof #"0& for $0 months. :ind the rate of interest

compounded monthly.


31/37

-.) An item can be purchased for # $-'"&& or

for # 1'0&& down payment and installment

payment of # $'&1& for 1* months. :ind theinterest rate compounded semi3 annually.

".) A trust fund is to be formed by depositin#-'"&& every quarter for " 2 years in a bank

that promises to pay a fied rate over the

entire term. If the amount of the fund at the

end of the term is # 0"'&&& find the rate

compounded quarterly.


32/37

:indin the 7>?M of

an Annuity


33/37

+oro borrows #%&'&&& with interestat "." compounded quarterly. !e

arees to pay #0"& at the end of

each quarter. !ow lon must hepay


34/37

Ms. Marie Abellar invest her retirementbenefits of 1.0 million at 4

compounded monthly. If she withdraws

the money in monthly payments of

#"&'&&&' how many reular payments

will she et


35/37

:ind the time and the number of semi3

annual payments of #-0& each and the

concludin deposit' which must be made

to accumulate #$0'"&&' if money earns

interest at , compounded semi3

annually.


36/37

A man deposits # "'%&& at the end

of each three months in an account

payin $- converted quarterly. In

order to accumulate #$&"'&&&' howmany reular deposit every quarter

must he make and what is the si@e of

the concludin payment' if one isneeded


37/37

Annuity Due ' !ormulas

Finding F when given A

Finding P when given A

+=

+

11)1( 1

i

iAF

n

++= + 1)1(1

1

i

iAP

n

lesson 4 - annuity (ordinary).pptx

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